The optical Berry phase and the Gauss-Bonnet theorem

The rotation of the plane of polarization of light in an optical fibre whose initial and final directions are parallel is given by the Berry phase, as interpreted by Chiao and Wu (1986) and observed by Tomita and Chiao (1986). It is shown that this result follows directly from geometrical considerations, by appealing to the Gauss-Bonnet theorem in the tangent space of the fibre.